1. What is Inverse Tangent?

The inverse tangent (arctangent) function calculates the angle whose tangent is a given number. For tan(θ) = 1, the principal value is θ = 45° or π/4 radians.

2. How Does the Calculator Work?

The calculator uses the mathematical function:

Where:

• \( x \) — Input value (ratio of opposite/adjacent sides)
• \( \theta \) — Resulting angle in selected units

Explanation: The function returns the principal value between -90° and 90° (or -π/2 and π/2 radians).

3. Importance of Inverse Tangent

Details: Inverse tangent is essential in trigonometry, physics, engineering, and computer graphics for converting slope ratios back to angles.

4. Using the Calculator

Tips: Enter any real number value and select your preferred output unit (degrees or radians). The calculator will return the corresponding angle.

5. Frequently Asked Questions (FAQ)

Q1: Why is arctan(1) equal to 45°?
A: Because tan(45°) = 1 (opposite and adjacent sides are equal in a right triangle at 45°).

Q2: What's the range of arctan function?
A: The principal value range is -90° to 90° (-π/2 to π/2 radians).

Q3: How is this different from arcsin or arccos?
A: Each inverse trig function returns angles for different ratios - arctan uses opposite/adjacent ratio.

Q4: When would I need this calculation?
A: Common applications include calculating angles from slopes, vector directions, and phase angles.

Q5: Can I calculate inverse tangent of very large numbers?
A: Yes, arctan approaches ±90° as the input approaches ±infinity.